ALPHA: probability of detecting a false effect (two sided: double this if you need one sided).

r: correlation coefficient for failure between paired subjects.

*: input either (P0 and RR) or (P0 and P1), where RR=P0/P1.

P0: event rate in the control group.

P1: event rate in experimental group.

RR: risk of failure of experimental subjects relative to controls.

Practical issues

Usual values for POWER are 80%, 85% and 90%; try several in order to explore/scope.

5% is the usual choice for ALPHA.

r can be estimated from previous studies - note that r is the phi (correlation) coefficient that is given for a two by two table if you enter it into the StatsDirect r by c chi-square function. When r is not known from previous studies, some authors state that it is better to use a small arbitrary value for r, say 0.2, than it is to assume independence (a value of 0) (Dupont, 1988).

P0 can be estimated as the population event rate. Note, however, that due to matching, the control sample is not a random sample from the population therefore population event rate can be a poor estimate of P0 (especially if confounders are strongly associated with the event).

If possible, choose a range of relative risks that you want have the statistical power to detect.

Technical validation

The estimated sample size n is calculated as:

- where α = alpha, β = 1 - power and zp is the standard normal deviate for probability p. n is rounded up to the closest integer.